a Check Figure 4 and Figure 2 by drawing line segments connecting the corresponding vertices of Figure 3.
B
b Which figure seems to be the reflection of Figure 4? Draw segments connecting the corresponding vertices of Figure 2.
C
c Use the following property of reflections: R_m(A)=A' if and only if R_m(A')=A.
A
aRule: Figure 3= R_j(Figure1) Explanation: See solution.
B
bRule: Figure 2= R_n(Figure4) Explanation: See solution.
C
cRule: Figure 4= R_n(Figure2) Explanation: See solution.
Practice makes perfect
a We want to write a reflection rule to describe Figure 3.
In the diagram, Figure 3 cannot be a reflection of Figure 4 because Figure 4 is not other side of the line j, nor line n. Let's check the other figures by drawing the line segments connecting the corresponding vertices.
We see that the lines j and n are not the perpendicular bisector of the segment drawn from Figure 3 to Figure 2. Thus, Figure 3 is not a reflection of Figure 2. However, line j is the perpendicular bisector of all the segments drawn from Figure 3 to Figure 1. Hence, Figure 3 is a reflection of Figure 1 across the line j.
Figure 3= R_j(Figure1)
b Looking at the diagram, it seems that Figure 2 is a reflection of Figure 4. Let's check it by drawing the line segments connecting the corresponding vertices.
We see that the line n is the perpendicular bisector of all the segments drawn from Figure 2 to Figure 4. Hence, Figure 2 is a reflection of Figure 4 across the line n.
Figure 2= R_n(Figure4)
c We will use the following property of reflections.
R_m(A)=A' if and only if R_m(A')=A
Using the rule in Part B and the property above, we can write a reflection rule to describe Figure 4.
Figure 2= R_n(Figure4)
⇕
Figure 4= R_n(Figure2)
